| Abstract: | The effectiveness of various analytical formulas for estimating R 2 shrinkage in multiple regression analysis was investigated. Two categories of formulas were identified: estimators of the squared population multiple correlation coefficient (ρ2) and those of the squared population cross-validity coefficient (ρc 2). The authors conducted a Monte Carlo experiment to investigate the effectiveness of the analytical formulas for estimating R 2 shrinkage, with 4 fully crossed factors (squared population multiple correlation coefficient, number of predictors, sample size, and degree of multicollinearity) and 500 replications in each cell. The results indicated that the most widely used Wherry formula (in both SAS and SPSS) is probably not the most effective analytical formula for estimating ρ2. Instead, the Pratt formula and the Browne formula outperformed other analytical formulas in estimating ρ2 and ρc 2, respectively. |
